d4fb58ae8a test: EC: optimize scalar multiplication of G by using lookup table (Sebastian Falbesoner)
1830dd8820 test: add secp256k1 module with FE (field element) and GE (group element) classes (Pieter Wuille)
Pull request description:
This PR rewrites a portion of `test_framework/key.py`, in a compatible way, by introducing classes that encapsulate field element and group element logic, in an attempt to be more readable and reusable.
To maximize readability, the group element logic does not use Jacobian coordinates. Instead, group elements just store (affine) X and Y coordinates directly. To compensate for the performance loss this causes, field elements are represented as fractions. This undoes most, but not all, of the performance loss, and there is a few % slowdown (as measured in `feature_taproot.py`, which heavily uses this).
The upside is that the implementation for group laws (point doubling, addition, subtraction, ...) is very close to the mathematical description of elliptic curves, and this extends to potential future extensions (e.g. ElligatorSwift as needed by #27479).
ACKs for top commit:
achow101:
ACK d4fb58ae8a
theStack:
re-ACK d4fb58ae8a
stratospher:
tested ACK d4fb58a. really liked how this PR makes the secp256k1 code in the tests more intuitive and easier to follow!
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